Chapter 1.4 ElementaryMatrices

We say a and b are row equivalent if each can be

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Unformatted text preview: nt if each can be obtained from the other by a finite sequence of row operations. Rephrase (c) of the theorem: Theorem An n × n matrix A is invertible if and only if A is row equivalent to In . Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Finding the Inverse of a Matrix Theorem If A is an invertible n × n matrix, and C = [A | In ], then rref (C ) = [In | A−1 ]. Proof. Er Er −1 · · · E1 A = In , where Ei is the elementary matrix corresponding to the i th elementary row operation in the sequence required to obtain In . Therefore, A−1...
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